A method of the kind described above has already been known for some time from the state of the art and is characterized by those working in the field as a “best fit adaptation”.
Usually, the desired geometry, which is to be checked on the workpiece to be measured, is pregiven. The pregiven desired geometry is defined by corresponding geometric parameters such as, for example, points to be contacted. If the test feature, which is to be determined from the measured actual geometry, is, for example, the diameter of a bore, which may not be less than a defined radial diameter, then one would define a circle having a pregiven minimum diameter as a desired geometry which is to be fitted.
Either the desired geometry or the actual geometry, which is defined by the measurement points measured on the workpiece, is then so rotated and shifted that these measurement points are fitted as optimally as possible one inside the other in order to then determine whether the deviation of the measured measurement points is sufficient relative to the fitted pregiven desired geometry. When the desired geometry is shifted, parameters for a rotation matrix as well as parameters for a translation vector are determined in this adaptation operation. These parameters describe the rotation and the translation of the pregiven desired geometry in the direction of the measured measurement points so that the desired geometry comes to lie on the measured points in the best possible manner. If, in contrast, the actual geometry is shifted, parameters for a rotation matrix as well as parameters for a translation vector are determined in this adaptation operation. These parameters describe the rotation and the translation of the actual geometry (or more precisely stated, the rotation and translation of the measurement points) in the direction of the pregiven desired geometry so that the measurement points come to lie on the pregiven desired geometry in the best possible manner.
Usually, the Gaussian method of least squares is used in order to determine these parameters. The parameters of the rotation matrix and of the translation vector are determined in such a manner that the sum of the distance squares between the measured measurement points and the pregiven desired geometry becomes minimal. Alternatively, the method of Tschebyscheff can be used wherein the maximum amount of the distance between a measured measurement point and the pregiven geometry is to be minimized or is to be fitted or adapted to a pregiven tolerance zone.
In somewhat different situations, as they result, for example, with bore diameters, scaling parameters can be provided in addition to the parameters describing the desired geometry. These scaling parameters define the scaling of the desired geometry or the actual geometry so that not only the parameters of the rotation matrix and translation vector are determined via the corresponding adaptation method, but also scaling parameters which define the scaling of the desired geometry or the actual geometry. One such scaling parameter is, for example, the radius of an adapted circle.
The deviations between the actually measured measurement points and a pregiven desired geometry can be determined in a relatively simple manner via the above-described well known methods. The known methods are, however, completely inadequate when the actual geometry of the workpiece, which is to be measured, deviates relative to the pregiven desired geometry. There are different reasons for this. On the one hand, workpieces, which are manufactured in the plastics industry, change their geometry over a long time after the actual manufacturing process. However, on the other hand, it is desirable to check as early as possible as to whether the pregiven manufacturing tolerances are maintained so that the manufacturing process can be readjusted as may be required. However, with conventional methods, it is not possible to simulate such changes of the manufactured workpiece.
A further example for such deviations is noted with respect to the deepdraw method for sheet metal. Here, stresses, which arise because of the deep-draw method, cause distortions of the workpiece. Even though the deep-drawn workpiece is not coincident with the pregiven desired geometry, the workpiece can nonetheless have the provided desired geometry when it was built in as required. Similar effects can occur with metal workpieces which become twisted because of the temperatures occurring during the manufacturing process and have their final form after complete cooling.
Workpieces having fluid dynamic profiles show a different problem, for example, the profile of a turbine vane or blade. The adaptation or fitting of a pregiven desired geometry of a turbine blade profile to the actual geometry of an actually measured turbine blade profile (which is defined by the measurement points) is often very problematic because the actually measured turbine blade profile is often shorter or longer than the pregiven desired geometry. The tolerances of the form deviations usually are very small, the permissible length deviations are, however, very large. For this reason, there is a contradiction between the form deviations and the length deviations especially in the area of an acute angle outlet edge of the turbine blade profile so that a purposeful adaptation of the desired geometry is therefore not possible.